I will not say that it is impossible to do it in 2 or 3 days, but I don't think that you would want to. Last time I was there, it was 3.5 days.
Permit? Yes, of course. Permits can be had at the Roads End permit station. However, it is a very popular route, and there is a lot of competition for the quota. So, permit reservations can be had, or else show up very early and be prepared to battle off the others standing in line for a walk-in permit.